A previously proposed electric brake system is described, for example, in German Published Patent Application No. 196 34 567. The brake system described there has a decentralized structure, where a pedal unit to form the reference input variable intended by the driver, optionally a processing unit for taking into account additional functions as well as wheel pair units to control or regulate the controlling elements of the wheel brakes are connected by one or more communication systems. Furthermore, the brake system receives power from at least two on-board electric systems. This guarantees sufficient safety and availability of the brake system. With this known system, wheel pair units are provided, and two wheel brakes are assigned to each unit. The wheel pair units each have essentially two microcomputers which monitor one another. Each microcomputer is assigned to another wheel brake and controls it according to the setpoints. The resulting operating reliability and availability are not optimal for all applications.